@aleo16, They only choose their own persona if they are "dumb" AI's. Cortana was one of the first "smart" AI's, which are created from an actual brain. "Smart" AI's inherit their mannerisms and personality from the brain of the person they are cloned from. An example would be that when Cortana told Halsey that she thought John (Master Chief) was cute when she was picking her spartan, Halsey blushed because she thought that too, and she couldn't deny it because Cortana reflected her opinions and personality.

Okay, while Steel is right about Cortana being created from a flash cloned brain of Halsey, AI's choose their own persona, or avatar (their look) immediately after they are created. Some make themselves look like gods, others like animals, and Cortana just chose to make herself look simple.